Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces. (18th October 2010) - Morii Morii, Kei Kei; Sato Sato, Tokushi Tokushi; Sawano Sawano, Yoshihiro Yoshihiro; Wadade Wadade, Hidemitsu Hidemitsu
Abstract : The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding W 1, n ( ℝ n ) ↪ L ∞ ( ℝ n ) fails for n ≥ 2 . Brézis-Gallouët-Wainger and some other authors quantified why this embedding fails by means of the Hölder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.